An efficient stochastic harmonic function approach for the simulation of 3-directional wind field of large wind turbines based on physical turbulent spectral model

Atmospheric boundary layer turbulent wind field is a typical 3-directional (3-D) random field with three turbulence components. Reasonable description and simulation of the 3-D turbulent wind field lay a significant foundation for the wind-induced response analysis and wind-resistance design of large wind turbines (WTs). In this study, a novel simulation method of the 3-D turbulent wind field for large WTs based on the stochastic harmonic function, physical turbulent spectrum and the rotational sampling scheme is proposed. The theoretical context of the physical spectral tensor based on the rapid distortion theory (RDT) of the uniform shear turbulent field is first introduced. Then the stochastic harmonic function (SHF) representation method is proposed to express the 3-D turbulence components as a summation of a series of harmonic components with random wavenumbers and phase angles, and the rotational sampling scheme is employed to reduce the number of spatial discretization points of the wind field. To further relieve the computing burden of the harmonic superposition, a two-step acceptance-rejection (A-R) scheme is proposed to reduce the wavenumber terms in the simulation formula, and the evolution phase model (EPM) is employed to reduce the dimension of the random phase angles. The proposed method is then validated through the numerical simulation of 3-D turbulent wind fields of a 5 MW WT, and the advantages of the proposed method in both efficiency and accuracy are revealed through comparisons with the conventional spectral representation approaches.